Simplify the following expression: $ z = \dfrac{r - 9}{-5r} + \dfrac{10}{7} $
Explanation: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{7}{7}$ $ \dfrac{r - 9}{-5r} \times \dfrac{7}{7} = \dfrac{7r - 63}{-35r} $ Multiply the second expression by $\dfrac{-5r}{-5r}$ $ \dfrac{10}{7} \times \dfrac{-5r}{-5r} = \dfrac{-50r}{-35r} $ Therefore $ z = \dfrac{7r - 63}{-35r} + \dfrac{-50r}{-35r} $ Now the expressions have the same denominator we can simply add the numerators: $z = \dfrac{7r - 63 - 50r}{-35r} $ $z = \dfrac{-43r - 63}{-35r}$ Simplify the expression by dividing the numerator and denominator by -1: $z = \dfrac{43r + 63}{35r}$